In this work, we undertake a thorough analysis of the estimation of the blind channel and apply the equalization technique based on subspaces. Addressing the challenges in modern digital communication systems employing QAM for multiple concurrent signal transmissions, we establish a robust signal model. Building upon this model, we introduce an innovative channel estimator that is based on subspace is designed to minimize a cost function. Our investigation delves into the asymptotic performance of this estimator, scrutinizing metrics such as bias, mean square error (MSE), NRMSE, and effecting of evaluation of the channel. Additionally, we evaluate the channel's effectiveness, providing insights into its prospective applications. The study contributes to advancing blind channel estimation and equalization techniques, offering potential applications in diverse communication scenarios.